It is on the restaurant to bring a new bottle. The cost is on them.
The couple times I have had it happen someone in the restaurant checked the wine to see if I was making it up (I wasn’t, it’s obvious when it is corked). But, bad is bad. It’d be like them serving you something rotten. It is on them to fix the problem and you do not pay for the mistake.
To be clear though…tasting the wine is only to see if it has gone bad (corked). You can’t (or shouldn’t) send it back just because you decide you don’t like it (but it is otherwise fine). And, as noted above, it is very rare these days a bottle will be bad. It was probably a common enough occurrence in the old days but very rare now.
A ‘corked’ wine will smell and taste like musty cardboard, wet dog, or a moldy basement. - SOURCE
All of this, of course, is when you are buying the whole bottle. Fine restaurants will often also have wine by the glass. If you are trying to decide which one to buy in that case, they will give you a little taste and you can turn it down if you don’t like it. Sometimes you will get a taste of two different ones and you can you choose the one you like best.
There’s a major distinction here between wine being corked or otherwise spoiled and the customer just not liking it. In the first case, the restaurant is absolutely responsible, in the second case, it’s ethically and legally the customer’s wine and the customer’s problem. Sending it back in such a case is at best extremely rude and how a restaurant handles it would depend on the particular restaurant and their relationship with the customer. The “little taste” that the sommelier pours into your glass is not to determine if you like it, it’s for you to make sure the wine hasn’t spoiled in some way.
If I was the head waiter and a customer raised a fuss and was refusing to pay for a bottle they just didn’t like, I would inform them that they weren’t going to be served and ask them to leave. But that’s just me; I have no tolerance for assholes. I would feel that this is the sort of customer who might send an entire expensive meal back because they just didn’t like that, either. No thanks, that kind of customer nobody needs.
A lot of Southeast Asians can’t metabolize alcohol. I knew several. One would just turn bright red and get hot. Another would actually get sick. The one who turns red was born in Hong Kong and didn’t come to the US until his early teens. He said “everybody knows” Chinese can’t drink wine, as your waiter did. Maybe it’s truism in China? Was your waiter an immigrant?
OTOH, I’ve also known a ton of Chinese and AB Chinese who had no problem with drinking wine at all.
One Christmas, my BiL served me a bottle of wine he got as a gift from one of the doctors he worked for. It was delicious! I drank most of the bottle. Later, he thought I wanted more and opened a bottle he’d gotten from TJ’s. I didn’t finish the glass. I was really easier to tell the better wine (which was the more expensive one, not completely unsurprisingly).
Usually, but they may be able to push back on their distributor. Especially if there is a pattern of bad corkage from a particular winery. We once sent a corked bottle back and the sommelier remarked that they’d had more than one bad bottle from that case.